It is known that when a two-wheeled vehicle takes a curvilinear trajectory, it tilts on its side internal to the bend forming an angle defined as "camber" angle, the value of which can reach 65.degree. with respect to the vertical plane of the ground; due to this operation, tires give rise to a camber thrust counteracting the centrifugal force acting on the vehicle.
Originally, tires had a carcass structure comprising a pair of plies of rubberized fabric reinforced with cords symmetrically inclined to the equatorial plane of the tire, usually known as cross-ply carcass structure, and optionally a belting structure also made of pairs of rubberized fabric strips with cords angled to the equatorial plane of the tire.
This carcass structure was capable of developing important camber thrusts; in addition, the tire pair had a very homogeneous behavior on a bend in that although the two tires had different sizes, they exerted qualitatively similar camber thrusts which were largely sufficient to balance the centrifugal thrust acting on the vehicle.
Driving the vehicle on a bend therefore was not particularly difficult, in that the vehicle had neutral driving characteristics so that a driver could take a curvilinear trajectory almost instinctively, by merely tilting the vehicle, without making adjustments to the attitude thereof, in particular the steering angle of the handlebar.
In confirmation of the above, motorcyclists surely can remember that they could go along a bend without holding the handlebar with their hands, but by merely moving their own center of gravity.
In contrast, problems existed in terms of ride comfort, stability, vehicle roadholding and driver fatigue, connected with an excessive stiffness of the tires. The tire structure, under the effect of an imposed deformation, stores up spring energy that is instantaneously returned when stresses stop, thereby amplifying disturbances transmitted from the road surface, which results in loss of stability on the part of the vehicle. In particular when running takes place on a straight road, this excessive stiffness causes oscillations of high frequency (8-10 Hz) on the front tire at low speed (shimmy effect) and oscillations of lower frequency (3-4 Hz) on the vehicle at high speed, so that driving becomes precarious.
In an attempt to obviate these problems, the use of radial-carcass tires having a belt structure made of textile or metallic cords has been recently introduced. In particular, the rear tire is provided with a belt structure comprising (sometimes in an exclusive manner) winding of cords preferably of metal, oriented in a circumferential direction, whereas the front tire has a belt structure provided with radially overlapped strips of inclined cords.
Surely this pair of tires has improved the situation in terms of ride comfort and driving stability. Oscillations of the vehicle at high speed on a straight stretch practically have disappeared, in that the rear tire has an important damping effect, while the shimmy effect substantially remained unchanged.
The behavior improvement on a straight stretch however has triggered a new problem, namely, the radial structure of the tire, in combination with a belt of circumferentially disposed cords (at 0.degree.) is unable to give rise to a camber thrust suitable for requirements, also taking into account the increasingly higher performance offered by vehicles.
More particularly, the rear tire furnishes a lower and qualitatively different thrust (that is of a linear type) than that (which is curvilinear) of the front tire. Consequently, the thus equipped vehicles have lost a neutral behavior and acquired an over-steering behavior. Thus, on a bend the rear wheel, unable to counteract the centrifugal force of increasing value acting on the axis, at a certain point skids, that is tends to come out of its trajectory moving to the outside of the bend whereas the front tire closes to the inside of the bend.
In other words, as the speed increases and the radius of curvature of the trajectory decreases, the vehicle inclination alone is no longer sufficient to compensate for the effect of the centrifugal force. Thus, the vehicle inclination is no longer sufficient for ensuring a running stability. Thus, increase in the thrust exerted by the tires is required and this increase is obtained by varying the vehicle attitude by an operation carried out by the driver by means of the handlebar, usually known to those skilled in the art as "push steer", that is by inclining the rolling plane of the front tire with respect to the tangential direction of the curvilinear trajectory through an angle, called "slip angle" directed in a direction opposite to the trajectory curvature.
Thus a full thrust is obtained which is the sum of a camber thrust resulting from the inclination of the equatorial plane of the tire relative to the vertical line and a slip camber caused by the angular variation of the rolling plane of the front wheel.
The value to be assigned to the slip angle depends on the structural and behavioral features of the front tire, that is on the link that the tire is capable of express between the slip angle value and the slip thrust value, in combination with its camber thrust and the thrust exerted by the rear tire.
On coming out of a bend, in contrast, an opposite operation is necessary, which is usually referred to by those skilled in the art as "pull steer": i.e. the handlebar is to be inclined to the inside of the bend so as to lift the motor-vehicle up and follow the rectilinear trajectory again. As a result of the above, the vehicle behavior is greatly conditioned by the tire pair with which it is equipped, which pair must be therefore conveniently selected and verified.
Attempts to facilitate this task have already been made. Patent EP 280,889 offers a method of carrying out this selection a prior without further experimental controls being required. In accordance with the teachings of this patent, if one defines as .delta..sub.1 and .delta..sub.2 the slip responses, that is those functions linking the slip angle with the slip thrust for the front and rear tires respectively, tire pairs for which function .delta..sub.2 -.delta..sub.1 appears to be an increasing monotonic function of the vehicle shift angle will be acceptable.
Actually the method does not solve the problem because the slip response also depends on the inflating pressure of the tire and in any case the result does not have an absolute value. In fact, there were pairs of tires that came out to be unacceptable in spite of the fact that they complied with the stated rule and vice-versa.